Side AB and AC of triangle ABC are produced in P & Q respectively. Bisectors of exterior angle CBP and BCQ meet at O. Show that AO bisects angle BAC.!!!!
2006-10-25 16:14:52 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Okay, this might be difficult to do without illustrations but here I go. It is given that point O is on two separate angle bisectors: angle OBC is the angle bisector for PBC and OCB is the angle bisector for QCB. Okay, since point o lies on both these angle bisectors, the distance from o to BC is the same as the distance from o to p; similarly, the distance from o to line q is the same as these first two distances. By transitivity, the distance from o to line p is the same as the distance from o to line q; because line p and q meet at point a, this means that o must lie on the angle bisector of a: so oa must bisect angle a.
Hope this was good enough to understand.
2006-10-26 02:31:33 · answer #1 · answered by bruinfan 7 · 1⤊ 0⤋
i have a better question...
does this apply in real life situations...will it apply in a real life situation...will it be on paper...will anyone care...will the world go smoother without ever figuring it out?
is there an easier way to describe what you're trying to find
2006-10-25 16:20:29 · answer #2 · answered by Mr.RIGHT 2 · 0⤊ 3⤋
omg what a brain teaser . what the ****has this got to do with everyday life stuff ?
2006-10-25 16:35:06 · answer #3 · answered by bonehead 2 · 0⤊ 2⤋